

A294444


Number of distinct numbers appearing as denominators in row n of Kepler's triangle A294442.


2



1, 1, 1, 2, 3, 6, 10, 16, 29, 51, 83, 148, 246, 402, 650, 1084, 1740, 2803, 4458
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OFFSET

0,4


COMMENTS

It would be nice to have a formula or recurrence.


LINKS

Table of n, a(n) for n=0..18.


EXAMPLE

Row 4 of A294442 contains eight fractions,
1/5, 4/5, 3/7, 4/7, 2/7, 2/7, 3/8, 5/8.
There are three distinct denominators, so a(4) = 3.


MAPLE

# S[n] is the list of fractions, written as pairs [i, j], in row n of Kepler's triangle; nc is the number of distinct numerators, and dc the number of distinct denominators
S[0]:=[[1, 1]]; S[1]:=[[1, 2]];
nc:=[1, 1]; dc:=[1, 1];
for n from 2 to 18 do
S[n]:=[];
for k from 1 to nops(S[n1]) do
t1:=S[n1][k];
a:=[t1[1], t1[1]+t1[2]];
b:=[t1[2], t1[1]+t1[2]];
S[n]:=[op(S[n]), a, b];
od:
listn:={};
for k from 1 to nops(S[n]) do listn:={op(listn), S[n][k][1]}; od:
c:=nops(listn); nc:=[op(nc), c];
listd:={};
for k from 1 to nops(S[n]) do listd:={op(listd), S[n][k][2]}; od:
c:=nops(listd); dc:=[op(dc), c];
od:
nc; # A294443
dc; # A294444


CROSSREFS

Cf. A294442, A294443.
See A293160 for a similar sequence related to the SternBrocot triangle A002487.
Sequence in context: A034419 A201864 A198200 * A066895 A105075 A140669
Adjacent sequences: A294441 A294442 A294443 * A294445 A294446 A294447


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane, Nov 20 2017


STATUS

approved



